This article on the Physics Archive blog cites a paper whose premise is that the fact that we don't typically see quantum effects (like superposition of states) at the macroscopic level (roughly defined as those systems made up of a number of quantum particles above Avogadro's Number) may imply that P != NP [*].

https://medium.com/the-physics-ar…

I have only a dilettante's knowledge of either quantum physics or computational complexity theory, but this is a _really_ interesting idea.

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[*] That is, there is no possible algorithm that can be computed in polynomial time for problems whose known algorithms are computable in non-polynomial time, for example, factoring very large numbers, a principle upon which modern encryption schemes are based.